document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=980070>Question 980070</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two trains made the same 150-mile run. Since one train traveled 20 mph faster than the other, it arrived 2 hours earlier. Find the speed of each train. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601276 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52769)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=601276\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Let &nbsp;<B>u</B>&nbsp; be the speed of the faster train in mph (miles per hour).\r<BR>\n" );
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document.write( "Then the speed of the other train is &nbsp;<B>u</B>-20 mph.\r<BR>\n" );
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document.write( "We have an equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150%2Fu ALIGN=MIDDLE  ALT=\"150%2Fu\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150%2F%28u-20%29 ALIGN=MIDDLE  ALT=\"150%2F%28u-20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2.\r<BR>\n" );
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document.write( "Solve this equation by simplifying it step by step:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150%28u-20%29 ALIGN=MIDDLE  ALT=\"150%28u-20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150u ALIGN=MIDDLE  ALT=\"150u\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2u%28u-20%29 ALIGN=MIDDLE  ALT=\"2u%28u-20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150u ALIGN=MIDDLE  ALT=\"150u\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3000 ALIGN=MIDDLE  ALT=\"3000\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=150u ALIGN=MIDDLE  ALT=\"150u\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2u%5E2 ALIGN=MIDDLE  ALT=\"2u%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40u ALIGN=MIDDLE  ALT=\"40u\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2u%5E2 ALIGN=MIDDLE  ALT=\"2u%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40u ALIGN=MIDDLE  ALT=\"40u\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3000 ALIGN=MIDDLE  ALT=\"3000\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E2 ALIGN=MIDDLE  ALT=\"u%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20u ALIGN=MIDDLE  ALT=\"20u\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1500 ALIGN=MIDDLE  ALT=\"1500\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "You can solve this quadratic equation by using quadratic formula &nbsp;(see the lesson &nbsp;<A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/quadratic/lessons/Introduction-Into-Quadratics.lesson>Introduction into Quadratic Equations</A>&nbsp; in this site). \r<BR>\n" );
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document.write( "Or, &nbsp;you can solve it by applying the Viete's formula &nbsp;(see the lesson &nbsp;<A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/quadratic/lessons/Solving-quadratic-equations-without-quadratic-formula.lesson>Solving quadratic equations without quadratic formula</A>&nbsp; in this site). \r<BR>\n" );
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document.write( "In any case, &nbsp;the roots of the quadratic equation are &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5B1%5D ALIGN=MIDDLE  ALT=\"u%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 50 mph &nbsp;and  &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5B2%5D ALIGN=MIDDLE  ALT=\"u%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = -30 mph. \r<BR>\n" );
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document.write( "Only positive value of the speed has the sense in this problem, &nbsp;so that the solution is &nbsp;u = 50 mph.\r<BR>\n" );
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document.write( "<B>Answer</B>. &nbsp;The speed of the faster train is &nbsp;50 mph. &nbsp;The speed of the other train is &nbsp;30 mph. \r<BR>\n" );
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document.write( " </SPAN>\n" );
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